How to use camera distance to mix textures?
You can use the camera data node to control the mixture of two nodes (color mix or shader mix).

Mix nodes expect information on the 0 to 1 scale, so the distance information will need to be scaled somehow or you need to define a threshold for the transition.

As an example: With a math node in "Less Than" or "More Than" mode you can create a distance threshold for the transition.



For a more subtle transition you can use a gradient texture:

Notice that you can usel Z depth as well and use a multiply node to control the transition point.



And for more control a color ramp.



For more info read : Using the Camera Data Node